Optimal inference for nonlinear latent structures in networks and tensors

Develop computationally tractable and statistically optimal procedures for nonlinear latent-factor structures in symmetric network data and tensor data.

Background

The paper develops a computationally tractable, statistically optimal inference pipeline for generalized latent factor models with missing entries in rectangular data matrices. The authors note that analogous nonlinear latent structures naturally arise in symmetric network data and tensor data, where the proposed methodology does not directly apply.

The unresolved issue is whether procedures with both computational tractability and statistical optimality can be constructed for these broader data structures. This extends the paper’s central concerns—nonlinearity, missingness, optimization, and uncertainty quantification—to network and tensor settings.